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It has been well known that the quantum zero‐point energy (ZPE) cannot be conserved in simulations of atoms and molecules dynamics based on classical mechanics. The purpose of this paper is to examine fundamental issues related to the treatment of quantum ZPE constraint in simulations of atoms and molecules dynamics.

The ZPE is well known to be a quantum mechanical expectation value that is equivalent to an ensemble average when this value is interpreted to classical mechanics. An important point is that the ensemble‐averaged energies on simulations are expected to obey the ZPE criteria rather than those of individual simulation. The point is elucidated using quasiclassical trajectory calculations with a popular hydrogen atom‐diatom direct collision process incorporating a potential energy surface of a triatomic hydrogen system.

The results obtained by using standard classical trajectory calculations agree well with the quantum calculations. Using them, the author found that the classical results remain valid even if some trajectory calculations have vibrational energies that are less than the ZPE.

It is found that the ensemble‐average of each trajectory calculation can provide results that are consistent with quantum mechanical ones that obey the ZPE criteria, without the introduction of any additional constraint conditions for atoms and simulation algorithms.

This paper aims to describe the physical and numerical modeling of a new computational fluid dynamics solver for hypersonic flows in thermo-chemical non-equilibrium. The code uses a blend of numerical techniques to ensure accuracy and robustness and to provide scalability for advanced hypersonic physics and complex three-dimensional (3D) flows.

The solver is based on an edge-based stabilized finite element method (FEM). The chemical and thermal non-equilibrium systems are loosely-coupled to provide flexibility and ease of implementation. Chemical non-equilibrium is modeled using a laminar finite-rate chemical kinetics model while a two-temperature model is used to account for thermodynamic non-equilibrium. The systems are solved implicitly in time to relax numerical stiffness. Investigations are performed on various canonical hypersonic geometries in two-dimensional and 3D.

The comparisons with numerical and experimental results demonstrate the suitability of the code for hypersonic non-equilibrium flows. Although convergence is shown to suffer to some extent from the loosely-coupled implementation, trading a fully-coupled system for a number of smaller ones improves computational time. Furthermore, the specialized numerical discretization offers a great deal of flexibility in the implementation of numerical flux functions and boundary conditions.

The FEM is often disregarded in hypersonics. This paper demonstrates that this method can be used successfully for these types of flows. The present findings will be built upon in a later paper to demonstrate the powerful numerical ability of this type of solver, particularly with respect to robustness on highly stretched unstructured anisotropic grids.

Partially‐decoupled upwind‐based total‐variation‐diminishing (TVD) finite‐difference schemes for the solution of the conservation laws governing two‐dimensional non‐equilibrium vibrationally relaxing and chemically reacting flows of thermally‐perfect gaseous mixtures are presented. In these methods, a novel partially‐decoupled flux‐difference splitting approach is adopted. The fluid conservation laws and species concentration and vibrational energy equations are decoupled by means of a frozen flow approximation. The resulting partially‐decoupled gas‐dynamic and thermodynamic subsystems are then solved alternately in a lagged manner within a time marching procedure, thereby providing explicit coupling between the two equation sets. Both time‐split semi‐implicit and factored implicit flux‐limited TVD upwind schemes are described. The semi‐implicit formulation is more appropriate for unsteady applications whereas the factored implicit form is useful for obtaining steady‐state solutions. Extensions of Roe's approximate Riemann solvers, giving the eigenvalues and eigenvectors of the fully coupled systems, are used to evaluate the numerical flux functions. Additional modifications to the Riemann solutions are also described which ensure that the approximate solutions are not aphysical. The proposed partially‐decoupled methods are shown to have several computational advantages over chemistry‐split and fully coupled techniques. Furthermore, numerical results for single, complex, and double Mach reflection flows, as well as corner‐expansion and blunt‐body flows, using a five‐species four‐temperature model for air demonstrate the capabilities of the methods.

To compute the Navier‐Stokes equations of a non‐equilibrium weakly ionized air flow. This can help to have a better description of the flow‐field and the wall heat transfer in hypersonic conditions.

The numerical approach is based on a multi block finite volume method and using a Riemann's solver based on a MUSCL‐TVD algorithm. In the flux splitting procedure the modified speed of sound, due to the electronic mode, is implemented.

A good description of the shock standoff distance, of the wall heat fluxes and of the peak of electron density number in the shock layer.

The radiative effects are not included in this paper. For the very high Mach numbers, this can modify the shock layer parameters.

The knowledge of the wall heat transfer in the re‐entry body problems.

The building of a robust numerical code in order to well describe hypersonic air flow in high Mach numbers.

The Fay and Riddell (F–R) formula is an empirical equation for estimating the stagnation-point heat flux on noncatalytic and fully catalytic surfaces, based on an assumption of equilibrium. Because of its simplicity, the F–R has been used extensively for reentry flight design as well as ground test facility applications. This study aims to investigate the uncertainties of the F-R formula by considering velocity gradient, chemical species at the boundary layer edge, and the thermochemical nonequilibrium (NEQ) behind the shock layer under various hypersonic NEQ flow environments.

The stagnation-point heat flux calculated with the F–R formula was evaluated by comparison with thermochemical NEQ calculations and existing flight experimental values.

The comparisons showed that the F–R underestimated the noncatalytic heat flux, because of the chemical composition at the surface. However, for fully catalytic heat flux, the F–R results were similar to values of surface heat flux from thermochemical NEQ calculations, because the F–R formula overestimates the diffusive heat flux. When compared with the surface heat flux results obtained from flight experimental data, the F–R overestimated the fully catalytic heat flux. The error was 50% at most.

The results provided guidelines for the F–R calculations under hypersonic flight conditions and for determining the approximate error range for noncatalytic and fully catalytic surfaces.

ABM Chemicals Ltd is exhibiting its range of photosensitisers for uv curing including the Glocure benzoin ethers. These highly cost effective materials ensure maximum utilisation of uv energy for the polymerisation process.

Points out that differences in the background of the working population, are often made responsible for the observed inequality of income distribution. Explores whether the observed distribution in incomes in countries such as the Federal Republic of Germany (West and East), Great Britain, Sweden, the United States and Brazil could not be the result of a statistical distribution process in which households participate. Recalls the early work in statistical thermodynamics by Boltzmann and Maxwell, who studied the distribution of energy among an ensemble of identical molecules, and which showed that not all molecules hold the same energy, but rather that the distribution has an exponential fall‐off character, with most molecules being in the lower energy bracket. Adapts the Maxwell‐Boltzmann distribution to incomes, and transforms these distributions into well‐known Lorenz graphs, and obtains a perfect match for each examined country. Suggests that, as the distributions can be directly related to their corresponding statistical weights, and as their logarithms are proportional to entropy in statistical thermodynamics, it could be shown that the unequal income distribution has a higher entropy, and therefore is more stable than the corresponding low entropy distribution resulting from Boulding′s principle of equal advantage where all households earn the same income. Supposes that neither of the two extreme stand‐points to explain the inequality of incomes can lead to a totally satisfactory explanation. Proposes that evolutionary strategies may be an interesting lead to follow up in more detail.

The purpose of the paper is to analyse the performances of closures and compressibility corrections classically used in turbulence models when applied to highly-compressible turbulent boundary layers (TBLs) over flat plates.

A direct numerical simulation (DNS) database of TBLs, covering a wide range of thermodynamic conditions, is presented and exploited to perform a priori analyses of classical and recent closures for turbulent models. The results are systematically compared to the “exact” terms computed from DNS.

The few compressibility corrections available in the literature are not found to capture DNS data much better than the uncorrected original models, especially at the highest Mach numbers. Turbulent mass and heat fluxes are shown not to follow the classical gradient diffusion model, which was shown instead to provide acceptable results for modelling the vibrational turbulent heat flux.

The main originality of the present paper resides in the DNS database on which the a priori tests are conducted. The database contains some high-enthalpy simulations at large Mach numbers, allowing to test the performances of the turbulence models in the presence of both chemical dissociation and vibrational relaxation processes.

WHEN the temperature of the gas reaches the high level, the molecules begin to break up into atoms or groups of atoms, which after recombination form new and smaller molecules of a simpler structure. For instance, tri‐atomic molecules after having been split form diatomic ones. This process is called the dissociation of gases. The newly‐formed molecules, when colliding, again form molecules of the original gas, so two processes are occurring simultaneously. However, the higher the temperature, the larger the percentage of dissociated molecules.

A finite difference method for solving the quasi one‐dimensional non‐equilibrium hypersonic flow equations in a diverging nozzle is presented and discussed. In chemically reacting flows the system of equations to be solved is very stiff. Some reactions may be several orders of magnitude faster than others and generally, they are much faster than the convective process except for very high Ma numbers. For this reason the development of a numerical scheme whose stability is independent of the chemical reaction rates is of importance. The main advantage of this scheme is the conservation of each chemical component, the positivity of densities and vibrational energies, as well as its relative simplicity, which results in a fast computer code.