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Nonequilibrium flow computations. I - An analysis of numerical formulations of conservation laws

Modern numerical techniques employing properties of flux Jacobian matrices are extended to general, nonequilibrium flows. Generalizations of the Beam-Warming scheme, Steger-Warming and van Leer Flux-vector splittings, and Roe's approximate Riemann solver are presented for 3-D, time-varying grids. The analysis is based on a thermodynamic model that includes the most general thermal and chemical nonequilibrium flow of an arbitrary gas. Various special cases are also discussed.

Liu, Yen↗

Perspectives on hypersonic viscous and nonequilibrium flow research

An attempt is made to reflect on current focuses in certain areas of hypersonic flow research by examining recent works and their issues. Aspects of viscous interaction, flow instability, and nonequilibrium aerothermodynamics pertaining to theoretical interest are focused upon. The field is a diverse one, and many exciting works may have either escaped the writer's notice or been abandoned for the sake of space. Students of hypersonic viscous flow must face the transition problems towards the two opposite ends of the Reynolds or Knudsen number range, which represents two regimes where unresolved fluid/gas dynamic problems abound. Central to the hypersonic flow studies is high-temperature physical gas dynamics; here, a number of issues on modelling the intermolecular potentials and inelastic collisions remain the obstacles to quantitative predictions. Research in combustion and scramjet propulsion will certainly be benefitted by advances in turbulent mixing and new computational fluid dynamics (CFD) strategies on multi-scaled complex reactions. Even for the sake of theoretical development, the lack of pertinent experimental data in the right energy and density ranges is believed to be among the major obstacles to progress in aerothermodynamic research for hypersonic flight. To enable laboratory simulation of nonequilibrium effects anticipated for transatmospheric flight, facilities capable of generating high enthalpy flow at density levels higher than in existing laboratories are needed (Hornung 1988). A new free-piston shock tunnel capable of realizing a test-section stagnation temperature of 10(exp 5) at Reynolds number 50 x 10(exp 6)/cm is being completed and preliminary tests has begun (H. Hornung et al. 1992). Another laboratory study worthy of note as well as theoretical support is the nonequilibrium flow experiment of iodine vapor which has low activation energies for vibrational excitation and dissociation, and can be studied in a laboratory with modest resources (Pham-Van-Diep et al. 1992).

Cheng, H. K.↗

Recent developments on time-dependent calculation of nonequilibrium flows

It is shown that, in a time-dependent nonequilibrium flow analysis, erroneous and unstable solutions can result from the use of temperature equations and flow variables other than pressure in fitting the bow shock. A formulation is presented that has been critically evaluated by comparison with a previous one and found to yield steady and more accurate solutions in conserving total enthalpy.

Li, C. P.↗

A survey of simulation and diagnostic techniques for hypersonic nonequilibrium flows

The possible means of simulating nonequilibrium reacting flows in hypersonic environments, and the required diagnostic techniques, are surveyed in two categories: bulk flow behavior and determination of chemical rate parameters. Flow visualization of shock shapes for validation of computational-fluid dynamic calculations is proposed. The facilities and the operating conditions necessary to produce the required nonequilibrium conditions, the suitable optical techniques, and their sensitivity requirements, are surveyed. Shock-tubes, shock-tunnels, and ballistic ranges in a wide range of sizes and strengths are found to be useful for this purpose, but severe sensitivity requirements are indicated for the optical instruments, which can be met only by using highly-collimated laser sources. Likewise, for the determination of chemical parameters, this paper summarizes the quantities that need to be determined, required facilities and their operating conditions, and the suitable diagnostic techniques and their performance requirements. Shock tubes of various strengths are found to be useful for this purpose. Vacuum ultraviolet absorption and fluorescence spectroscopy and coherent anti-Stokes Raman spectroscopy are found to be the techniques best suited for the measurements of the chemical data.

Sharma, Surendra P.↗

Radiative coupled nonequilibrium flow fields associated with aeroassisted orbital transfer

Development of an algorithm which will allow nonequilibrium flow field codes to be coupled to radiative transfer codes (currently limited to equilibrium applications) was initiated. The algorithm consists of an equation for the prediction of electronic state population fractions (electronic state temperature) and equations for the computation of spectral absorption coefficients and source functions. These expressions represent a thorough treatment in the context of the bandless model which in the past has proven adequate for equilibrium radiative transfer predictions. Perhaps the approach is more than adequate as the current algorithm requires four temperatures for each transition. Clearly, a more sophisticated model can be developed; however, it would require more information, such as rotational temperatures of the electronic levels.

Horton, T. E.↗

An implementation of a chemical and thermal nonequilibrium flow solver on unstructured meshes and application to blunt bodies

This paper presents a nonequilibrium flow solver, implementation of the algorithm on unstructured meshes, and application to hypersonic flow past blunt bodies. Air is modeled as a mixture of five chemical species, namely O2, N2, O, NO, and N, having two temperatures namely translational and vibrational. The solution algorithm is a cell centered, point implicit upwind scheme that employs Roe's flux difference splitting technique. Implementation of this algorithm on unstructured meshes is described. The computer code is applied to solve Mach 15 flow with and without a Type IV shock interference on a cylindrical body of 2.5mm radius representing a cowl lip. Adaptively generated meshes are employed, and the meshes are refined several times until the solution exhibits detailed flow features and surface pressure and heat flux distributions. Effects of a catalytic wall on surface heat flux distribution are studied. For the Mach 15 Type IV shock interference flow, present results showed a peak heat flux of 544 MW/m2 for a fully catalytic wall and 431 MW/m(exp 2) for a noncatalytic wall. Some of the results are compared with available computational data.

Prabhu, Ramadas K.↗

Hypersonic, nonequilibrium flow over a cylindrically blunted 6 deg wedge

The numerical simulation of hypersonic flow in chemical nonequilibrium over cylindrically blunted 6 degree wedge is described. The simulation was executed on a Cray C-90 with Program LAURA 92-vl. Code setup procedures and sample results, including grid refinement studies and variations of species number are discussed. This simulation relates to a study of wing leading edge heating on transatmospheric vehicles.

Gnoffo, Peter A.↗

Hypersonic, nonequilibrium flow over the FIRE 2 forebody at 1634 sec

The numerical simulation of hypersonic flow in thermochemical nonequilibrium over the forebody of the FIRE 2 vehicle at 1634 sec in its trajectory is described. The simulation was executed on a Cray C90 with the program Langley Aerodynamic Upwind Relaxation Algorithm (LAURA) 4.0.2. Code setup procedures and sample results, including grid refinement studies, are discussed. This simulation relates to a study of radiative heating predictions on aerobrake type vehicles.

Chambers, Lin Hartung↗

Radiative interactions in nonequilibrium flows

The influence of vibrational and chemical nonequilibrium upon infrared radiative energy transfer in nonisothermal gases is investigated. Essential information is provided on rate equations, relaxation times, transfer equations, band absorption, and radiative flux equations. The methodology developed is applied to three specific cases. These are, absorbing-emitting species between isothermal parallel plates, radiating gases in the earth's atmosphere, and supersonic flow of premixed hydrogen and air in an expanding nozzle. The results obtained for different cases reveal that the extent of radiative interactions is reduced significantly under nonequilibrium conditions. The method developed can be easily extended to investigate radiative interactions in complex nonequilibrium flows.

Tiwari, S. N.↗

Predicting radiative heat transfer in thermochemical nonequilibrium flow fields. Theory and user's manual for the LORAN code

The theory for radiation emission, absorption, and transfer in a thermochemical nonequilibrium flow is presented. The expressions developed reduce correctly to the limit at equilibrium. To implement the theory in a practical computer code, some approximations are used, particularly the smearing of molecular radiation. Details of these approximations are presented and helpful information is included concerning the use of the computer code. This user's manual should benefit both occasional users of the Langley Optimized Radiative Nonequilibrium (LORAN) code and those who wish to use it to experiment with improved models or properties.

Chambers, Lin Hartung↗

Three-dimensional thermochemical nonequilibrium flow modeling for hypersonic flows

A three-dimensional thermochemical nonequilibrium model has been developed and applied to the study of entry flows surrounding space vehicles. The model accounts for both chemical and vibrational nonequilibrium phenomena behind the bow shock. The thermodynamic state of a real gas is modeled with a translational-rotational temperature and a electron-vibrational temperature. Their internal energies are averaged to determine the temperature used in the reaction rates calculation. In order to establish the validity of the selected models, both one- and two-temperature models with seven and/or eleven species were investigated. Several numerical experiments that include a sphere, the RAMC vehicle and 3D AFE forebody flows were performed. Preliminary results were compared with RAMC-II experimental data. Good agreement was obtained after a two-temperature model with eleven species and thirty reactions was incorporated into the study.

Tam, L. T.↗

Molecular-Based Optical Diagnostics for Hypersonic Nonequilibrium Flows

This presentation package consists of seven different talks rolled up into one. These talks are all invited orals presentations in a special session at the Aviation 2015 conference and represent contributions that were made to a recent AIAA book that will be published entitled 'Hypersonic Nonequilibrium Flows: Fundamentals and Recent Advances'. Slide 5 lists the individual presentations that will be given during the special session.

Paul Danehy↗

Time Accurate Simulation of Nonequilibrium Flow inside the NASA Ames Electric Arc Shock Tube

Numerical investigations of the ow field inside NASA Ames' Electric Arc Shock Tube have been performed. The focus is to simulate the experiments designed to reproduce shock layer radiation layer relevant to Earth re-entry conditions. This paper assess the current computational capability in simulating unsteady nonequilibrium flows in the presence of strong shock waves with state-of-the-art physical models. The technical approach is described with preliminary results presented for one specific ow condition. The numerical problems encountered during the computation of these flows are detailed, along with the methods used to resolve them. Post-shock conditions are discussed and compared to CEA equilibrium prediction.

Bensassi, Khalil↗

Time Accurate Simulation of Nonequilibrium Flow Inside the NASA Ames Electric Arc Shock Tube

Numerical investigations of the flowfield inside NASA Ames' Electric Arc Shock Tube have been performed. The focus is to simulate the experiments designed to reproduce shock layer radiation layer relevant to Earth re-entry conditions. This paper assess the current computational capability in simulating time-accurate unsteady nonequilibrium flows in the presence of strong shock waves with state-of-the-art physical models. The technical approach is described with preliminary results presented for one specific flow condition. It was found that the axisymmetric source term generates a numerical instability that appears as shock bending. This instability is time dependent which greatly affects the shock speed. Post-shock conditions are discussed and compared to CEA equilibrium prediction and good agreement was obtained close to the test-section and just behind the shock.

Bensassi, Khalil↗