Heats of transport of ideal gases and gas mixtures
Ideal gases and binary monatomic gas mixtures heats of transport derivation from kinetic theory expressions for thermal transpiration
Malinauskas, A. P.↗
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A method for calculating a real-gas two-dimensional nozzle contour including the effects of gamma
A method for calculating two-dimensional inviscid nozzle contours for a real gas or an ideal gas by the method of characteristics is described. The method consists of a modification of an existing nozzle computer program. The ideal-gas nozzle contour can be calculated for any constant value of gamma. Two methods of calculating the center-line boundary values of the Mach number in the throat region are also presented. The use of these three methods of calculating the center-line Mach number distribution in the throat region can change the distance from the throat to the inflection point by a factor of 2.5. A user's guide is presented for input to the computer program for both the two-dimensional and axisymmetric nozzle contours.
Johnson, C. B.↗
Flowfield computation of an aerobrake orbital transfer vehicle
Viscous real gas and ideal gas supersonic flowfields over the forebody of a aeroassisted orbital transfer vehicle are determined using a unsteady factored implicit algorithm. Air in chemical equilibrium is considered and its local thermodynamic properties are computed by an equilibrium composition method. Numerical solutions are obtained for both real and ideal gases at a Mach number of 30 and at angles of attack up to 20 degrees. Shock stand-off distances and surface pressure distributions are presented for the gas models with and without viscous effects. For the freestream conditions considered, viscous effects dominate the flow.
Balakrishnan, A.↗
Computational flow predictions for hypersonic drag devices
The effectiveness of two types of hypersonic decelerators is examined: mechanically deployable flares and inflatable ballutes. Computational fluid dynamics (CFD) is used to predict the flowfield around a solid rocket motor (SRM) with a deployed decelerator. The computations are performed with an ideal gas solver using an effective specific heat ratio of 1.15. The results from the ideal gas solver are compared to computational results from a thermochemical nonequilibrium solver. The surface pressure coefficient, the drag, and the extend of the compression corner separation zone predicted by the ideal gas solver compare well with those predicted by the nonequilibrium solver. The ideal gas solver is computationally inexpensive and is shown to be well suited for preliminary design studies. The computed solutions are used to determine the size and shape of the decelerator that are required to achieve a drag coefficient of 5. Heat transfer rates to the SRM and the decelerators are predicted to estimate the amount of thermal protection required.
Tokarcik, Susan A.↗
3-D plume flow computations with an upwind solver
In the present study multi-nozzle plume flows are computed with a three-dimensional, Navier-Stokes solver. Numerical simulations are performed with the flux-split, two-factor, time symptotic, viscous flow solver. The two factor splitting provides a stable three-dimensional solution procedure under ideal-gas assumptions. Viscous, ideal-gas solutions for a thin lip symmetrical nozzle are compared with experimental and numerical solutions. Computed solutions to axisymmetric and three-dimensional, multi-nozzle problems at various altitudes and flight conditions demonstrate flow field complexity and three-dimensional effects.
Venkatapathy, Ethiraj↗
Shock wave structure in an ideal dissociating gas
Composition changes within the shock layer due to chemical reactions are considered. The Lighthill ideal dissociating gas model was used in an effort to describe the oxygen type molecule. First, the two limiting cases, when the chemical reaction rates are very slow and very fast in comparison to local convective rates, are investigated. Then, the problem is solved for arbitrary chemical reaction rates.
Liu, K. H.↗
Real-Gas Correction Factors for Hypersonic Flow Parameters in Helium
The real-gas hypersonic flow parameters for helium have been calculated for stagnation temperatures from 0 F to 600 F and stagnation pressures up to 6,000 pounds per square inch absolute. The results of these calculations are presented in the form of simple correction factors which must be applied to the tabulated ideal-gas parameters. It has been shown that the deviations from the ideal-gas law which exist at high pressures may cause a corresponding significant error in the hypersonic flow parameters when calculated as an ideal gas. For example the ratio of the free-stream static to stagnation pressure as calculated from the thermodynamic properties of helium for a stagnation temperature of 80 F and pressure of 4,000 pounds per square inch absolute was found to be approximately 13 percent greater than that determined from the ideal-gas tabulation with a specific heat ratio of 5/3.
Erickson, Wayne D.↗
AFE base flow computations
Hypersonic wake flows behind the Aeroassist Flight Experiment (AFE) geometry are analyzed using two Navier-Stokes flow solvers. Many of the AFE wake features observed in ballistic-range shadowgraphs are simulated using a simple, two-dimensional semicylinder geometry at moderate angles of attack. At free-stream conditions corresponding to a Hypersonic Free Flight Facility (HFFF) AFE experiment, the three-dimensional base flow for the AFE geometry is computed using an ideal-gas, Navier-Stokes solver. The computed results agree reasonably well with the shadowgraphs taken at the HFFF. An ideal-gas and a nonequilibrium Navier-Stokes solver have been coupled and applied to the complete flow around the AFE vehicle at the free-stream conditions corresponding to a nomial trajectory point. Limitations of the coupled ideal-gas and nonequilibrium solution are discussed. The nonequilibrium base flow solution is analyzed for the wake radiation and the radiation profiles along various lines of sight are compared. Finally, the wake unsteadiness is predicted using experimental correlations and the numerical solutions. An adaptive grid code, SAGE, has been used in all the simulations to enhance the solution accuracy. The grid adaptation is found to be necessary in obtaining base flow solutions with accurate flow features.
Venkatapathy, Ethiraj↗
Computational flow predictions for hypersonic drag devices
The effectiveness of two types of hypersonic decelerators are computationally examined: mechanically deployable flares and inflatable ballutes. CFD is used to predict the flowfield around a solid rocket motor (SRM) with a deployed decelerator. The computations are performed with an ideal gas solver using an effective specific heat ratio of 1.15. The surface pressure coefficients, the drag, and the extent of the compression corner separation zone predicted by the ideal gas solver compare well with those predicted by the nonequilibrium solver. The ideal gas solver is computationally inexpensive and is shown to be well suited for preliminary design studies. The computed solutions are used to determine the size and shape of the decelerator that are required to achieve a drag coefficient of 5 in order to assure that the SRM will splash down in the Pacific Ocean. Heat transfer rates to the SRM and the decelerators are predicted to estimate the amount of thermal protection required.
Tokarcik, Susan↗
Effects of various assumptions on the calculated liquid fraction in isentropic saturated equilibrium expansions
The saturated equilibrium expansion approximation for two phase flow often involves ideal-gas and latent-heat assumptions to simplify the solution procedure. This approach is well documented by Wegener and Mack and works best at low pressures where deviations from ideal-gas behavior are small. A thermodynamic expression for liquid mass fraction that is decoupled from the equations of fluid mechanics is used to compare the effects of the various assumptions on nitrogen-gas saturated equilibrium expansion flow starting at 8.81 atm, 2.99 atm, and 0.45 atm, which are conditions representative of transonic cryogenic wind tunnels. For the highest pressure case, the entire set of ideal-gas and latent-heat assumptions are shown to be in error by 62 percent for the values of heat capacity and latent heat. An approximation of the exact, real-gas expression is also developed using a constant, two phase isentropic expansion coefficient which results in an error of only 2 percent for the high pressure case.
Bursik, J. W.↗
Thermodynamic properties and theoretical rocket performance of hydrogen to 100,000 K and 1.01325 x 10 to the 8th power N/sq m
The composition and thermodynamic properties were calculated for 100 to 110,000 K and 1.01325 x 10 to the 2nd power to 1.01325 x 10 to the 8th power N/sq m for chemical equilibrium in the Debye-Huckel and ideal-gas approximations. Quantities obtained were the concentrations of hydrogen atoms, protons, free electrons, hydrogen molecules, negative hydrogen ions, hydrogen diatomic molecular ions, and hydrogen triatomic molecular ions, and the enthalpy, entropy, average molecular weight, specific heat at constant pressure, density, and isentropic exponent. Electronically excited states of H and H2 were included. Choked, isentropic, one-dimensional nozzle flow with shifting chemical equilibrium was calculated to the Debye-Huckel and ideal-gas approximations for stagnation temperatures from 2500 to 100,000 K. The mass flow per unit throat area and the sonic flow factor were obtained. The pressure ratio, temperature, velocity, and ideal and vacuum specific impulses at the throat and for pressure ratios as low as 0.000001 downstream were found. For high temperatures at pressures approaching 1.01325 x 10 to the 8th power N/sq m, the ideal-gas approximation was found to be inadequate for calculations of composition, precise thermodynamic properties, and precise nozzle flow. The greatest discrepancy in nozzle flow occurred in the exit temperature, which was as much as 21 percent higher when the Debye-Huckel approximation was used.
Patch, R. W.↗
Analysis of transient heat transfer through a collisionless gas enclosed between parallel plates.
Transient heat transfer through monatomic collisionless ideal gas enclosed between parallel walls analyzed for step change in one wall temperature
MONATOMIC GAS↗
A theoretical analysis of simulated transonic boundary layers in cryogenic-nitrogen wind tunnels
A theoretical analysis was made to determine the real gas effects on simulation of transonic boundary layers in wind tunnels with cryogenic nitrogen as the test gas. The analysis included laminar and turbulent flat plate boundary layers and turbulent boundary layers on a two dimensional airfoil. The results indicate that boundary layers in such wind tunnels should not be substantially different from ideal gas boundary layers at standard conditions. At a pressure of 9.0 atm, two separate effects produce deviations of real gas values from ideal gas values which are in the opposite direction from deviations at 1.0 atm and are of the same insignificant order of magnitude. Results also show that nonadiabatic boundary layers should be adequately simulated if the enthalpy ratio is the correlating parameter rather than the temperature ratio.
Adcock, J. B.↗
Compressible Flow Toolbox
The Compressible Flow Toolbox is primarily a MATLAB-language implementation of a set of algorithms that solve approximately 280 linear and nonlinear classical equations for compressible flow. The toolbox is useful for analysis of one-dimensional steady flow with either constant entropy, friction, heat transfer, or Mach number greater than 1. The toolbox also contains algorithms for comparing and validating the equation-solving algorithms against solutions previously published in open literature. The classical equations solved by the Compressible Flow Toolbox are as follows: The isentropic-flow equations, The Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), The Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section), The normal-shock equations, The oblique-shock equations, and The expansion equations.
Melcher, Kevin J.↗
Thermodynamic Properties of Nitrogen Including Liquid and Vapor Phases from 63K to 2000K with Pressures to 10,000 Bar
Tables of thermodynamic properties of nitrogen are presented for the liquid and vapor phases for temperatures from the freezing line to 2000K and pressures to 10,000 bar. The tables include values of density, internal energy, enthalpy, entropy, isochoric heat capacity, isobaric heat capacity velocity of sound, the isotherm derivative, and the isochor derivative. The thermodynamic property tables are based on an equation of state, P=P (p,T), which accurately represents liquid and gaseous nitrogen for the range of pressures and temperatures covered by the tables. Comparisons of property values calculated from the equation of state with measured values for P-p-T, heat capacity, enthalpy, latent heat, and velocity of sound are included to illustrate the agreement between the experimental data and the tables of properties presented here. The coefficients of the equation of state were determined by a weighted least squares fit to selected P-p-T data and, simultaneously, to isochoric heat capacity data determined by corresponding states analysis from oxygen data, and to data which define the phase equilibrium criteria for the saturated liquid and the saturated vapor. The vapor pressure equation, melting curve equation, and an equation to represent the ideal gas heat capacity are also presented. Estimates of the accuracy of the equation of state, the vapor pressure equation, and the ideal gas heat capacity equation are given. The equation of state, derivatives of the equation, and the integral functions for calculating derived thermodynamic properties are included.
Thermodynamic properties↗
Numerical simulation of hypersonic, axisymmetric flowfields
Flow conditions corresponding to those of three previously conducted hypersonic axisymmetric flow experiments are presently treated by numerical solutions of the axisymmetric, thin layer Navier-Stokes equations with the Chemistry and Gasdynamic Implicit computer code's Version 2. While simulation and experimental results agree for ideal gas flows, the simulation for the case of a real gas flow reveals that the particular coupling of the gasdynamics and the chemistry used in the code degrades the convergence level obtainable, by comparison with ideal gas cases. The computed stagnation point heating is 60 percent lower than for the experiment.
Green, M. J.↗
User Guide for Compressible Flow Toolbox Version 2.1 for Use With MATLAB(Registered Trademark); Version 7
This report provides a user guide for the Compressible Flow Toolbox, a collection of algorithms that solve almost 300 linear and nonlinear classical compressible flow relations. The algorithms, implemented in the popular MATLAB programming language, are useful for analysis of one-dimensional steady flow with constant entropy, friction, heat transfer, or shock discontinuities. The solutions do not include any gas dissociative effects. The toolbox also contains functions for comparing and validating the equation-solving algorithms against solutions previously published in the open literature. The classical equations solved by the Compressible Flow Toolbox are: isentropic-flow equations, Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section.), normal-shock equations, oblique-shock equations, and Prandtl-Meyer expansion equations. At the time this report was published, the Compressible Flow Toolbox was available without cost from the NASA Software Repository.
Melcher, Kevin J.↗
One-dimensional flows of an imperfect diatomic gas
With the assumptions that Berthelot's equation of state accounts for molecular size and intermolecular force effects, and that changes in the vibrational heat capacities are given by a Planck term, expressions are developed for analyzing one-dimensional flows of a diatomic gas. The special cases of flow through normal and oblique shocks in free air at sea level are investigated. It is found that up to a Mach number 10 pressure ratio across a normal shock differs by less than 6 percent from its ideal gas value; whereas at Mach numbers above 4 the temperature rise is considerable below and hence the density rise is well above that predicted assuming ideal gas behavior. It is further shown that only the caloric imperfection in air has an appreciable effect on the pressures developed in the shock process considered. The effects of gaseous imperfections on oblique shock-flows are studied from the standpoint of their influence on the life and pressure drag of a flat plate operating at Mach numbers of 10 and 20. The influence is found to be small. (author)
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