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Chapman, Dean R.

Publications and source records attributed to Chapman, Dean R..

16 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

A Numerical Investigation of the Burnett Equations Based on the Second Law

The Burnett equations have been shown to potentially violate the second law of thermodynamics. The objective of this investigation is to correlate the numerical problems experienced by the Burnett equations to the negative production of entropy. The equations have had a long history of numerical instability to small wavelength disturbances. Recently, Zhong corrected the instability problem and made solutions attainable for one dimensional shock waves and hypersonic blunt bodies. Difficulties still exist when attempting to solve hypersonic flat plate boundary layers and blunt body wake flows, however. Numerical experiments will include one-dimensional shock waves, quasi-one dimensional nozzles, and expanding Prandlt-Meyer flows and specifically examine the entropy production for these cases.

Comeaux, Keith A.↗
NASA NTRS1993

Viscous hypersonic shock-shock interaction on a blunt body at high altitude

The shock interaction produced when an incident oblique shock impinges on a blunt body, such as an engine inlet cowl lip of a hypersonic vehicle, is investigated for high altitude flight conditions. A perfect gas, Navier-Stokes numerical simulation of this problem at various altitudes representing continuum through transitional conditions is performed using the modified flux vector splitting method of Steger and Warming (1979). Two series of solutions are produced. First, a number-of-shock-positions are studied at a particular altitude and Mach number. Second, given a fixed shock position and Mach number, the interaction is investigated at several altitudes ranging from continuum to transitional flow conditions. It is shown that the interaction becomes fundamentally different as the density is lowered, and its effect on the overheating problem is progressively diminished. The maximum stagnation point heating at the highest altitude is reached only when the incident shock misses the cowl lip completely, and any interaction with the cowl bow shock that does occur takes place downstream and thus has little effect on the conditions at the stagnation point.

Comeaux, Keith A.↗
NASA NTRS1992

A more accurate nonequilibrium air radiation code - NEQAIR second generation

Two experiments, one an equilibrium flow in a plasma torch at Stanford, the other a nonequilibrium flow in a SDIO/IST Bow-Shock-Ultra-Violet missile flight, have provided the basis for modifying, enhancing, and testing the well-known radiation code, NEQAIR. The original code, herein termed NEQAIR1, lacked computational efficiency, accurate data for some species and the flexibility to handle a variety of species. The modified code, herein termed NEQAIR2, incorporates recent findings in the spectroscopic and radiation models. It can handle any number of species and radiative bands in a gas whose thermodynamic state can be described by up to four temperatures. It provides a new capability of computing very fine spectra in a reasonable CPU time, while including transport phenomena along the line of sight and the characteristics of instruments that were used in the measurements. Such a new tool should allow more accurate testing and diagnosis of the different physical models used in numerical simulations of radiating, low density, high energy flows.

Moreau, Stephane↗
NASA NTRS1991

Accuracy of the Burnett equations for hypersonic real gas flows

Burnett solutions for the structure of normal shock waves for Mach numbers ranging from 1.1 to 50 have been obtained by using the time-dependent equation set in conjunction with modern computational fluid dynamic techniques. The current work seeks to provide corrected and improved high-resolution direct simulation Monte Carlo (DSMC) results for hypersonic shocks in monatomic gases. These DSMC results will serve as a reliable test base for assessing the accuracy of various continuum equations more advanced than Navier-Stokes, such as the Burnett equations. The main conclusion of Fisko and Chapman (1988) that the Burnett equations are more accurate than the Navier-Stokes equations for all gases and at all Mach numbers in matching DSMC shock wave results is reassesed by comparing the improved and corrected DSMC results with continuum Burnett results. Various Burnett results for shocks in a diatomic gas, nitrogen, which include improvements to the work of Lumpkin and Chapman (1989) are presented. It is concluded that the Burnett equations represent a significant improvement over Navier-Stokes equations for flows exhibiting translational nonequilibrium.

Lumpkin, Forrest E., III↗
NASA NTRS1989

Comparison of Burnett, super-Burnett and Monte Carlo solutions for hypersonic shock structure

The continuum Navier-Stokes, Burnett, and super-Burnett equations are solved for one-dimensional shock structures in various monoatomic gases. Solutions for a hard sphere gas, argon, and a Maxwellian gas from Mach 1.3 to Mach 50 are obtained. A numerical method utilizing the complete time-dependent continuum equations and obtaining the steady-state shock structure by allowing the system to relax from arbitrary initial conditions is employed. Shock density, velocity, temperature, and entropy profiles are also obtained using the direct simulation Monte Carlo method, and these results are used as bases for comparison for continuum solution profiles. It is shown that the Burnett equations yield shock structure solutions in much closer agreement to both Monte Carlo and experimental results than do the Navier-Stokes equations. Solutions to the super-Burnett equations with coefficients as presently derived, however, are considered to be inferior to those of the Burnett equations.

Fiscko, Kurt A.↗
NASA NTRS1988

Hypersonic shock structure with Burnett terms in the viscous stress and heat flux

The continuum Navier-Stokes and Burnett equations are solved for one-dimensional shock structure in various monatomic gases. A new numerical method is employed which utilizes the complete time-dependent continuum equations and obtains the steady-state shock structure by allowing the system to relax from arbitrary initial conditions. Included is discussion of numerical difficulties encountered when solving the Burnett equations. Continuum solutions are compared to those obtained utilizing the Direct Simulation Monte Carlo method. Shock solutions are obtained for a hard sphere gas and for argon from Mach 1.3 to Mach 50. Solutions for a Maxwellian gas are obtained from Mach 1.3 to Mach 3.8. It is shown that the Burnett equations yield shock structure solutions in much closer agreement to both Monte Carlo and experimental results than do the Navier-Stokes equations. Shock density thickness, density asymmetry, and density-temperature separation are all more accurately predicted by the Burnett equations than by the Navier-Stokes equations.

Chapman, Dean R.↗
NASA NTRS1988

Fundamental problem in computing radiating flow fields with thick shock waves

Possible reasons for the failure of the Navier-Stokes equations to yield realistic profiles of the temperature and density through the structure of a hypersonic shock wave are investigated. Models for bulk viscosity in a monatomic gas are examined which yield a realistic thickness for the shock-wave density profile, but not the temperature profile, and hence are not satisfactory. A tentative computational model for nitrogen is explored which yields considerably more realistic results than the Navier-Stokes equations. This model involves a nonlinear stress-strain tensor, nonlinear heat flux vector, and nonequilibrium rotational energy.

Chapman, Dean R.↗
NASA NTRS1988

Comparison of shock structure solutions using independent continuum and kinetic theory approaches

A vehicle traversing the atmosphere will experience flight regimes at high altitudes in which the thickness of a hypersonic shock wave is not small compared to the shock standoff distance from the hard body. When this occurs, it is essential to compute accurate flow field solutions within the shock structure. In this paper, one-dimensional shock structure is investigated for various monatomic gases from Mach 1.4 to Mach 35. Kinetic theory solutions are computed using the Direct Simulation Monte Carlo method. Steady-state solutions of the Navier-Stokes equations and of a slightly truncated form of the Burnett equations are determined by relaxation to a steady state of the time-dependent continuum equations. Monte Carlo results are in excellent agreement with published experimental data and are used as bases of comparison for continuum solutions. For a Maxwellian gas, the truncated Burnett equations are shown to produce far more accurate solutions of shock structure than the Navier-Stokes equations.

Fiscko, Kurt A.↗
NASA NTRS1987

Computational fluid dynamics near the continuum limit

Two dimensional Navier-Stokes equations for a perfect gas are solved for hypersonic flow over a flat plate at Reynolds numbers ranging from continuum to the free molecule flow. In the transition flow regime, new slip boundary conditions are introduced, which reduce to the well-known slip conditions of Maxwell at small Knudsen numbers and yield the correct shear stress and heat transfer in the limiting case of free molecule flow. Comparison of the computed results with the existing experimental data and Monte Carlo calculations indicates that the continuum Navier-Stokes equations give surprisingly realistic results throughout the transition flow regime, when the new slip boundary conditions are used.

Maccormack, Robert W.↗
NASA NTRS1962

Aerodynamic Heating and Deceleration During Entry into Planetary Atmospheres

Dr. Chapman's lecture examines the physics behind spacecraft entry into planetary atmospheres. He explains how scientists determine if a planet has an atmosphere and how scientists can compute deceleration when the atmospheric conditions are unknown. Symbols and equations used for calculations for aerodynamic heating and deceleration are provided. He also explains heat transfer in bodies approaching an atmosphere, deceleration, and the use of ablation in protecting spacecraft from high temperatures during atmospheric entry.

Chapman, Dean R.↗
NASA NTRS1962

Aerodynamic Evidence Pertaining to the Entry of Tektites into the Earth's Atmosphere

Evidence is presented which shows that the Australian and Java tektites entered the earth's atmosphere and experienced ablation by severe aerodynamic heating in hypervelocity flight. The laboratory experiments on hypervelocity ablation have reproduced ring-wave flow ridges and coiled circumferential flanges like those found on certain of these tektites. Systematic striae distortions exhibited in a thin layer beneath the front surface of australites also are reproduced in the laboratory ablation experiments, and are shown to correspond to the calculated distortions for aerodynamic ablation of a glass. About 98 percent of Australian tektites represent aerodynamically stable configurations during the ablative portion of an entry trajectory. Certain meteorites exhibit surface features similar to those on tektites.

AERODYNAMIC HEATING↗
NASA NTRS1960

An Analysis of the Corridor and Guidance Requirements for Supercircular Entry into Planetary Atmospheres

An analysis is presented of supercircular entry into a planet's atmosphere giving particular attention to the corridor through which spacecraft must be guided in order to accomplish various maneuvers. A dimensionless parameter based on conditions at the conic perigee altitude is introduced for characterizing supercircular entries and conveniently pre-scribing corridor widths associated with elliptic, parabolic, or hyperbolic approach trajectories. The analysis applies to vehicles of arbitrary weight, shape, and size. Illustrative calculations are made for Venus, Earth, Mars, Jupiter, and Titan. For nonlifting vehicles having fixed aerodynamic coefficients, curves are presented of dimensionless parameters from which can be calculated the maximum deceleration, maximum rate of laminar convective heating, and total laminar heat absorbed during single-pass entry at velocities up to twice circular velocity. For lifting vehicles, curves are presented of the maximum deceleration and overshoot boundary of an entry corridor; equations are presented for estimating laminar aerodynamic heating from the maximum deceleration. It is shown that the corridor width is independent of vehicle weight, dimensions, and drag coefficient, provided these are the same at the overshoot boundary as at undershoot. The corridors of certain planets can be broadened markedly by the application of aerodynamic lift; for example, the 10-earth-g corridor width for single- pass, nonlifting, parabolic entry is increased from 0 miles for Jupiter, 7 for Earth, and 8 for Venus, to 52, 51, and 52 miles, respectively, by employing a lift-drag ratio of 1. The use of aerodynamic lift does not increase appreciably the corridors of Mars and Titan. All corridor widths decrease rapidly as the entry velocity is increased. Terminal guidance requirements on accuracy of velocity and flight path angle for successfully entering various corridors are compared with analogous requirements for putting a satellite into orbit, for hitting the moon from the earth, and for achieving ICBM accuracy. Consideration is given to the terminal guidance problem involved in using a planet's atmosphere-rather than rocket fuel-to effect orbital transfers from heliocentric to planetocentric motion, thereby converting a hyperbolic approach trajectory to an elliptic orbit about the target planet. This fuel saving maneuver appears technologically feasible for certain planetary voyages, and implies the possibility of achieving a large reduction in required Earth lift-off weight of chemical propulsion systems.

Chapman, Dean R.↗
NASA NTRS1959

An Analysis of the Corridor and Guidance Requirements for Supercircular Entry into Planetary Atmospheres

The analysis of super-circular entry is developed around a new dimensionless parameter which combines certain conditions at the conic perigee altitude with certain characteristics of the vehicle; this parameter conveniently determines either deceleration-limited or heating limited corridor widths for elliptic, parabolic, or hyperbolic approach trajectories. Illustrative calculations of corridor widths and the associated guidance problems are presented for Venus, Earth, Mars, Jupiter, and Titan. Generalized curves are presented for application to various entry conditions.

Chapman, Dean R.↗
NASA NTRS1958

Turbulent Skin Friction at High Mach Numbers and Reynolds Numbers

For a number of years now, experimenters have been making measurements of skin friction. Formerly, the main interest was at low Mach numbers; later, measurements were made at supersonic Mach numbers. However, almost all of these measurements were over a limited range of Reynolds numbers. On the other hand, these measurements fairly well determined the effects of Mach number and heat transfer on skin friction. The purpose of this paper is to give the results of skin-friction measurements in turbulent boundary layers at high Mach numbers and high Reynolds numbers where data have not previously existed. The equipment used was expressly designed to provide these conditions. As is well known, it is difficult to obtain high Mach numbers and high Reynolds numbers simultaneously with air in a wind tunnel. In order to avoid condensation, it is necessary to heat the air, with a resulting loss in density and Reynolds number. It is desirable, then, to use a gas that does not condense at high Mach numbers. This suggested helium, which was used as a working fluid in some of the tests. At high Mach numbers in a given wind tunnel, higher Reynolds numbers can be obtained with helium than with air, principally because no heating of the helium is required. The different ratios of specific heats also contribute to the increase. In using helium as a working fluid, it is, of course, necessary to determine the equivalence of air and helium in the turbulent boundary layer.

Matting, Fred W.↗
NASA NTRS1951

Base Pressure on Wings and Bodies with Turbulent Boundary Layers

At present there is no satisfactory theory for calculating the pressure which acts at the blunt base of an object traveling at supersonic velocity. In fact, the essential mechanism determining the base pressure is only imperfectly understood. As a result, the existing knowledge of base pressure is based almost entirely on experiments. The main object of this paper is to summarize the principal results of the many wind tunnel and free flight measurements of base pressure on both bodies of revolution and blunt trailing edge airfoils. A relatively simple method of estimating base pressure is presented, and an indication is given as to how the characteristics of base pressure play an essential role in determining the shape of an aerodynamically efficient object for supersonic flight.

Chapman, Dean R.↗