K-DISTRIBUTION MODELS FOR GAS MIXTURES IN HYPERSONIC NONEQUILIBRIUM FLOWS

Open Access

Author:

Bansal, Ankit

Graduate Program:

Mechanical Engineering

Degree:

Doctor of Philosophy

Document Type:

Dissertation

Date of Defense:

October 19, 2011

Committee Members:

• Michael F. Modest, Committee Chair
• Daniel C. Haworth, Committee Chair
• Deborah A. Levin, Committee Member
• Stefan Thynell, Committee Member

Keywords:

• k-distribution
• spectral models
• Radiation
• shock layer
• Nonequilibrium
• Hypersonic
• OpenFOAM

Abstract:

Calculation of nonequilibrium radiation field in plasmas around a spacecraft entering into an atmosphere at hypersonic velocities is a very complicated and computationally expensive task. The objective of this Dissertation is to collect state-of-the art spectroscopic data for the evaluation of spectral absorption and emission coefficients of atomic and molecular gases, develop efficient and accurate spectral models and databases, and study the effect of radiation on wall heat loads and flowfield around the spacecraft. The most accurate simulation of radiative transport in the shock layer requires calculating the gas properties at a large number of wavelengths and solving the Radiative Transfer Equation (RTE) in a line-by-line (LBL) fashion, which is prohibitively expensive for coupled simulations. A number of k-distribution based spectral models are developed for atomic lines, continuum and molecular bands that allow efficient evaluation of radiative properties and heat loads in hypersonic shock layer plasma. Molecular radiation poses very different challenges than atomic radiation. A molecular spectrum is governed by simultaneous electronic, vibrational and rotational transitions, making the spectrum very strongly dependent on wavelength. In contrast to an atomic spectrum, where line wings play a major role in heat transfer, most of the heat transfer in molecular spectra occurs near line centers. As the first step, k-distribution models are developed separately for atomic and molecular species, taking advantage of the fact that in the Earth’s atmosphere the radiative field is dominated by atomic species (N and O) and in Titan’s and Mars’ atmospheres molecular bands of CN and CO are dominant. There are a number of practical applications where both atomic and molecular species are present, for example, the vacuum-ultra-violet spectrum during Earth’s reentry conditions is marked by emission from atomic bound-bound lines and continuum and simultaneous absorption by strong bands of N2. For such cases, a new model is developed for the treatment of gas mixtures containing atomic lines, continuum and molecular bands. Full-spectrum k-distribution (FSK) method provides very accurate results compared to those obtained from the exact line-by-line method. For cases involving more extreme gradients in species concentrations and temperature, full-spectrum k-distribution model is relatively less accurate, and the method is refined by dividing the spectrum into a number of groups or scales, leading to the development of multi-scale models. The detailed methodology of splitting the gas mixture into scales is presented. To utilize the full potential of the k-distribution methods, pre-calculated values of k-distributions are stored in databases, which can later be interpolated at local flow conditions. Accurate and compact part-spectrum k-distribution databases are developed for atomic species and molecular bands. These databases allow users to calculate desired full-spectrum k-distributions through look-up and interpolation. Application of the new spectral models and databases to shock layer plasma radiation is demonstrated by solving the radiative transfer equation along typical one-dimensional flowfields in Earth’s, Titan’s and Mars’ atmospheres. The k-distribution methods are vastly more efficient than the line-by-line method. The efficiency of the method is compared with the line-by-line method by measuring computational times for a number of test problems, showing typical reduction in computational time by a factor of more than 500 for property evaluation and a factor of about 32,000 for the solution of the RTE. A large percentage of radiative energy emitted in the shock-layer is likely to escape the region, resulting in cooling of the shock layer. This may change the flow parameters in the flowfield and, in turn, can affect radiative as well as convective heat loads. A new flow solver is constructed to simulate coupled hypersonic flow–radiation over a reentry vehicle. The flow solver employs a number of existing schemes and tools available in OpenFOAM; along with a number of additional features for high temperature, compressible and chemically reacting flows, and k-distribution models for radiative calculations. The radiative transport is solved with the one-dimensional tangent slab and P1 solvers, and also with the two-dimensional P1 solver. The new solver is applied to simulate flow around an entry vehicle in Martian atmosphere. Results for uncoupled and coupled flow–radiation simulations are presented, highlighting the effects of radiative cooling on flowfield and wall fluxes.