Daniil A. Andrienko

P1 Approximation Applied to the Radiative Heating of Descent Spacecraft

The P1 approximation of the spherical harmonics method is applied for the radiative heating calculation of space vehicles entering Mars’s atmosphere. Surface radiative heating of a spherical space vehicle and a Pathfinder-shape space vehicle in a viscous, heat conductive, and chemically nonequilibriumgasmixture is studied.Unstructured grids are used to integrate the radiation heat transfer equation. The multigroup spectral model is applied to describe the optical properties of absorbing and emitting media. The chemical model includes 10 species and 79 reactions. Two physically and chemically nonequilibriumpoints of trajectory are studied. Satisfactory agreement has been obtained between the P1 approximation and the ray-tracing method. Two algorithms have also been proposed to avoid physical inaccuracy of the P1 approximation in optically thin gas.

A computational approach for hypersonic nonequilibrium radiation utilizing space partition algorithm and Gauss quadrature

An efficient computational capability for nonequilibrium radiation simulation via the ray tracing technique has been accomplished. The radiative rate equation is iteratively coupled with the aerodynamic conservation laws including nonequilibrium chemical and chemical-physical kinetic models. The spectral properties along tracing rays are determined by a space partition algorithm of the nearest neighbor search process, and the numerical accuracy is further enhanced by a local resolution refinement using the Gauss-Lobatto polynomial. The interdisciplinary governing equations are solved by an implicit delta formulation through the diminishing residual approach. The axisymmetric radiating flow fields over the reentry RAM-CII probe have been simulated and verified with flight data and previous solutions by traditional methods. A computational efficiency gain nearly forty times is realized over that of the existing simulation procedures.

Spherical harmonics method applied to the multi-dimensional radiation transfer

Abstract The spectral radiation transfer equation in 2D axisymmetrical and 3D geometries is solved by the P 1 -approximation of the spherical harmonics and ray-tracing methods. Martian atmosphere and typical entry conditions are considered. Navier–Stokes equations coupled with the nonequilibrium vibrational excitation and finite rate chemistry describe thermodynamically and chemically nonequilibrium gas. The multi-group model is used to model optical properties of CO 2 –N 2 mixture. The developed methodology of integration of the P 1 -approximation on unstructured grids and subsequent numerical solution allow us to reach reasonable agreement with the accurate ray-tracing method and drastically reduce the cost of solution of the radiation transfer equation in multi-dimensional geometries.

Non-equilibrium flowfield of RAM-C II probe

A multi-temperature model is developed to investigate chemical composition of air plasma and heating rates at non-equilibrium points of RAM-C II probe trajectory. The vibrational energy of each molecular species and electron energy are described by individual conservation equation. Comparison with the experimental data provided by reflectometers and Langmuir probe and other theoretical works is presented. The developed model allows to obtain good agreement with the experimental data. The influence of the chemical mechanism, non-equilibrium model of dissociation and thermodynamic model is investigated. Convective heating rates in the wide range of altitude are reported.

Radiative heating of Martian space vehicle at crucial points of trajectory

The calculation of radiation heating rate with the use of the P1-approximation of spherical harmonics method is discussed in this paper. The finite-volume method is applied for triangular elements of the unstructured grids to integrate the radiation heat transfer equation. The two-dimensional axisymmetric geometry of the blunt cone body and spherical body is tested. The multigroup spectral model is implemented to describe the optical properties of absorbing and emitting media. The 10-species of carbon dioxide and nitrogen chemically active mixture is used to describe Martian atmosphere. Gasdynamic fields are obtained with the use of NERAT-2D.

Three-dimensional Radiative Heating of Descent Space Vehicle Based on Spherical Harmonics Method with Unstructured Grids

The P1-approximation of a spherical harmonics method is used to calculate the three dimensional radiative transfer in emitting and absorbing media for Martian descent space vehicle. The three dimensional governing system of equations describes the flow of viscous, heat conductive, chemically nonequilibrium and radiating CO2-N2 gas mixture. Detailed spectral model is used to calculate the forebody and afterbody radiative heating of capsule. Unstructured tetrahendronal grids are applied to build first order implicit scheme of radiation heat transfer equation. For this purpose highly effective iterative algorithm is applied to resolve sparse system of linear equations. Verification of presented algorithm is provided by tedious and accurate ray-tracing calculations.

View-Factor Approach as a Radiation Model for the Reentry Flowfield

An accurate and efficient radiation transfer model, based on the view-factor approach, is proposed for the reentry flowfield. The radiation transfer equation is coupled to the gasdynamic system of equations in order to describe the energy transfer in the absorbing and emitting air plasma in two-dimensional axisymmetric and three-dimensional geometries. A newly derived semi-analytical expression for the radiative flux density dramatically simplifies the calculation of the spectral and integral characteristics of the radiation flowfield in the axisymmetric geometry. The comparison with the ray-tracing method and tangent slab approximation revealed an asymptotic accuracy of radiation flux density.

On View-Factor Approach for Radiation Transfer Equation

View-factor approach is applied to calculate the radiation heating rates in some important engineering applications. The transfer of radiative energy is considered in the axisymmetric enclosure with the spherical temperature inhomogeneity and for the re-entry of the space vehicle. The numerical results by the view factor approach is then verified against the ray tracing method, diffusion and tangent slab approximations. Spectral radiative transfer on the surface of space vehicle during the orbital re-entry is resolved by means of the view-factor approach. An asymptotic accuracy of radiative flux density in two-dimensional axisymmetric geometry is demonstrated. Semi-analytical expression for the radiation flux density in two-dimensional geometry is derived. General recommendations are formulated for the application in the optically thin and thick media and for the application in three-dimensional geometry.

Compressible counter-flowing hydrogen-air combustion

The flow structural response to the diffusive non-premixed adiabatic flame generated by counter flowing jets of air and hydrogen is computationally investigated. The flame thickness and temperature are studied as functions of applied strain rates. The numerical approach includes solutions of compressible Navier-Stokes equations for the mean flow using an implicit ADI algorithm in delta form with TVD flux splitting formulation. The present numerical approach is comparing against the classic artificial compressibility method. A comprehensive investigation of simulations on influence of chemical model, transport properties, boundary conditions is also included. The computed results are found to give reasonable agreement with classical approach, however the flame front is found to be more diffusive. The flame thickness is found to be inversely proportional to a square root of strain rate and the deviation from this dependence at near extinction state is also studied. An extinction of combustion corresponding to the third explosion limit has been observed at high strain rate. I. Nomenclature a = strain rate, s -1 l = flame thickness, mm t = time, s