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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Thermodynamic properties of “near-perfect” gas

When applied thermodynamics requires simple representations of thermodynamic quantities, one often finds quantities such as pressure and the thermal energy density expressed as a monomial linear product of density and temperature power laws. This is a simple generalization of the product of density and temperature used for the perfect gas that admits a broader range of thermodynamic behavior into analytic fluid calculations or provides an analytic form that is readily fit to tabulated equation-of-state data for an arbitrary material. This paper reviews the thermodynamic properties of this generalized perfect-gas model, treating it as a class of “near-perfect-gas” models that are defined and unified here, for the first time, through a shared Helmholtz free energy. This generalization from perfect to near-perfect-gas models preserves some perfect-gas properties (e.g., constant adiabatic exponents) but not others (e.g., constant specific heats) and is constrained by thermodynamic consistency. It is important to be aware of the properties of this class of near-perfect-gas models when using them as surrogates for real nonperfect materials that may have properties that cannot be captured by near-perfect-gas models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1971

A computer program for two-dimensional and axisymmetric nonreacting perfect gas and equilibrium chemically reacting laminar, transitional and-or turbulent boundary layer flows

A computer program is described in detail for laminar, transitional, and/or turbulent boundary-layer flows of non-reacting (perfect gas) and reacting gas mixtures in chemical equilibrium. An implicit finite difference scheme was developed for both two dimensional and axisymmetric flows over bodies, and in rocket nozzles and hypervelocity wind tunnel nozzles. The program, program subroutines, variables, and input and output data are described. Also included is the output from a sample calculation of fully developed turbulent, perfect gas flow over a flat plate. Input data coding forms and a FORTRAN source listing of the program are included. A method is discussed for obtaining thermodynamic and transport property data which are required to perform boundary-layer calculations for reacting gases in chemical equilibrium.

Miner, E. W.↗
NASA NTRS1959

Numerical Solution of the Flow of a Perfect Gas Over A Circular Cylinder at Infinite Mach Number

A solution for the two-dimensional flow of an inviscid perfect gas over a circular cylinder at infinite Mach number is obtained by numerical methods of analysis. Nonisentropic conditions of curved shock waves and vorticity are included in the solution. The analysis is divided into two distinct regions, the subsonic region which is analyzed by the relaxation method of Southwell and the supersonic region which was treated by the method of characteristics. Both these methods of analysis are inapplicable on the sonic line which is therefore considered separately. The shapes of the sonic line and the shock wave are obtained by iteration techniques. The striking result of the solution is the strong curvature of the sonic line and of the other lines of constant Mach number. Because of this the influence of the supersonic flow on the sonic line is negligible. On comparison with Newtonian flow methods, it is found that the approximate methods show a larger variation of surface pressure than is given by the present solution.

Hamaker, Frank M.↗
NASA NTRS1975

Numerical solution of the hypersonic viscous-shock-layer equations for laminar, transitional, and turbulent flows of a perfect gas over blunt axially symmetric bodies

The viscous shock layer equations applicable to hypersonic laminar, transitional, and turbulent flows of a perfect gas over two-dimensional plane or axially symmetric blunt bodies are presented. The equations are solved by means of an implicit finite difference scheme, and the results are compared with a turbulent boundary layer analysis. The agreement between the two solution procedures is satisfactory for the region of flow where streamline swallowing effects are negligible. For the downstream regions, where streamline swallowing effects are present, the expected differences in the two solution procedures are evident.

Anderson, E. C.↗
NASA NTRS1994

Computer code for determination of thermally perfect gas properties

A set of one-dimensional compressible flow relations for a thermally perfect, calorically imperfect gas is derived for the specific heat c(sub p), expressed as a polynomial function of temperature, and developed into the thermally perfect gas (TPG) computer code. The code produces tables of compressible flow properties similar to those of NACA Rep. 1135. Unlike the tables of NACA Rep. 1135 which are valid only in the calorically perfect temperature regime, the TPG code results are also valid in the thermally perfect calorically imperfect temperature regime which considerably extends the range of temperature application. Accuracy of the TPG code in the calorically perfect temperature regime is verified by comparisons with the tables of NACA Rep. 1135. In the thermally perfect, calorically imperfect temperature regime, the TPG code is validated by comparisons with results obtained from the method of NACA Rep. 1135 for calculating the thermally perfect calorically imperfect compressible flow properties. The temperature limits for application of the TPG code are also examined. The advantage of the TPG code is its applicability to any type of gas (monatomic, diatomic, triatomic, or polyatomic) or any specified mixture thereof, whereas the method of NACA Rep. 1135 is restricted to only diatomic gases.

Witte, David W.↗
NASA NTRS1990

An upwind-biased, point-implicit relaxation algorithm for viscous, compressible perfect-gas flows

An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for three-dimensional, viscous, compressible, perfect-gas flows is described. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's Symmetric Total Variation Diminishing scheme. Viscous terms are discretized using central differences. The relaxation strategy is well suited for computers employing either vector or parallel architectures. It is also well suited to the numerical solution of the governing equations on unstructured grids. Because of the point-implicit relaxation strategy, the algorithm remains stable at large Courant numbers without the necessity of solving large, block tri-diagonal systems. Convergence rates and grid refinement studies are conducted for Mach 5 flow through an inlet with a 10 deg compression ramp and Mach 14 flow over a 15 deg ramp. Predictions for pressure distributions, surface heating, and aerodynamics coefficients compare well with experiment data for Mach 10 flow over a blunt body.

Gnoffo, Peter A.↗
NASA NTRS1987

Perfect gas effects in compressible rapid distortion theory

The governing equations presented for small amplitude unsteady disturbances imposed on steady, compressible mean flows that are two-dimensional and nearly uniform have their basis in the perfect gas equations of state, and therefore generalize previous results based on tangent gas theory. While these equations are more complex, this complexity is required for adequate treatment of high frequency disturbances, especially when the base flow Mach number is large; under such circumstances, the simplifying assumptions of tangent gas theory are not applicable.

Kerschen, E. J.↗
NASA NTRS1973

Analysis of a two-dimensional type 6 shock-interference pattern using a perfect-gas code and a real-gas code

Numerical codes were developed to calculate the two dimensional flow field which results when supersonic flow encounters double wedge configurations whose angles are such that a type 4 pattern occurs. The flow field model included the shock interaction phenomena for a delta wing orbiter. Two numerical codes were developed, one which used the perfect gas relations and a second which incorporated a Mollier table to define equilibrium air properties. The two codes were used to generate theoretical surface pressure and heat transfer distributions for velocities from 3,821 feet per second to an entry condition of 25,000 feet per second.

Bertin, J. J.↗
NASA NTRS2007

Turbulent Aeroheating Testing of Mars Science Laboratory Entry Vehicle in Perfect-Gas Nitrogen

An experimental investigation of turbulent aeroheating on the Mars Science Laboratory entry vehicle heat shield has been conducted in the Arnold Engineering Development Center Hypervelocity Wind Tunnel No. 9. Testing was performed on a 6-in. (0.1524 m) diameter MSL model in pure N2 gas in the tunnel s Mach 8 and Mach 10 nozzles at free stream Reynolds numbers of 4.1x10(exp 6)/ft to 49x10(exp 6)/ft (1.3x10(exp 7)/m to 16x10(exp 7)/m) and 1.2x10(exp 6)/ft to 19x10(exp 6)/ft (0.39x10(exp 7)/m to 62x10(exp 7)/m), respectively. These conditions were sufficient to span the regime of boundary-layer flow from completely laminar to fully-developed turbulent flow over the entire forebody. A supporting aeroheating test was also conducted in the Langley Research Center 20-Inch Mach 6 Air Tunnel at free stream Reynolds number of 1x10(exp 6)/ft to 7x10(exp 6)/ft (0.36x10(exp 7)/m to 2.2x10(exp 7)/m) in order to help corroborate the Tunnel 9 results. A complementary computational fluid dynamics study was conducted in parallel to the wind tunnel testing. Laminar and turbulent predictions were generated for all wind tunnel test conditions and comparisons were performed with the data for the purpose of helping to define uncertainty margins on predictions for aeroheating environments during entry into the Martian atmosphere. Data from both wind tunnel tests and comparisons with the predictions are presented herein. It was concluded from these comparisons that for perfect-gas conditions, the computational tools could predict fully-laminar or fully-turbulent heating conditions to within 10% of the experimental data

Hollis, Brian R.↗
NASA NTRS1968

Axisymmetric two-phase perfect gas performance program

Computer program calculates the inviscid axisymmetric nozzle expansion of propellant systems having both gaseous and condensed exhaust products. The program uses velocity and thermal lags and will perform calculations for contoured and conical nozzles.

Kliegel, J. R.↗
NASA NTRS1971

An Analytical Investigation of an Oscillating Wedge in a Supersonic Perfect Gas Flow

Several aspects of the oscillating wedge are investigated to evaluate both the resulting trends for the wedge and methods of analyzing unsteady flows. An existing hypersonic small disturbance theory for an oscillating thin wedge is extended and applied. A perturbation method involving linearization about the known flow is then derived and discussed. Subsequently, a finite difference technique for calculating the complete unsteady flow field of the wedge in motion is presented and discussed in conjunction with some calculated quasi-static nonlinear trends.

Bennett, R. M.↗
NASA NTRS1972

Computer program for solving compressible nonsimilar-boundary-layer equations for laminar, transitional, or turbulent flows of a perfect gas

A computer program is described which solves the compressible laminar, transitional, or turbulent boundary-layer equations for planar or axisymmetric flows. Three-point implicit difference relations are used to reduce the momentum and energy equations to finite-difference form. These equations are solved simultaneously without iteration. Turbulent flow is treated by the inclusion of either a two-layer eddy-viscosity model or a mixing-length formulation. The eddy conductivity is related to the eddy viscosity through a static turbulent Prandtl number which may be an arbitrary function of the distance from the wall boundary. The transitional boundary layer is treated by the inclusion of an intermittency function which modifies the fully turbulent model. The laminar-boundary-layer equations are recovered when the intermittency is zero, and the fully turbulent equations are solved when the intermittency is unity.

Price, J. M.↗
NASA NTRS1973

A computer program for calculating the perfect gas inviscid flow field about blunt axisymmetric bodies at an angle of attack of 0 deg

A method for the rapid calculation of the inviscid shock layer about blunt axisymmetric bodies at an angle of attack of 0 deg has been developed. The procedure is of an inverse nature, that is, a shock wave is assumed and calculations proceed along rays normal to the shock. The solution is iterated until the given body is computed. The flow field solution procedure is programed at the Langley Research Center for the Control Data 6600 computer. The geometries specified in the program are sphores, ellipsoids, paraboloids, and hyperboloids which may conical afterbodies. The normal momentum equation is replaced with an approximate algebraic expression. This simplification significantly reduces machine computation time. Comparisons of the present results with shock shapes and surface pressure distributions obtained by the more exact methods indicate that the program provides reasonably accurate results for smooth bodies in axisymmetric flow. However, further research is required to establish the proper approximate form of the normal momentum equation for the two-dimensional case.

Zoby, E. V.↗
NASA NTRS1978

Experimental perfect-gas study of expansion-tube flow characteristics

Results of an experimental investigation of expansion tube flow characteristics performed with helium test gas and acceleration gas are presented. The use of helium, eliminates complex real gas chemistry in the comparison of measured and predicted flow quantities. The driver gas was unheated helium at a nominal pressure of 33 MN sq m. The quiescent test gas pressure and quiescent acceleration gas pressure were varied from 0.7 to 50 kN/sq m and from 2.5 to 53 N/sq m, respectively. The effects of tube-wall boundary layer growth and finite secondary diaphragm opening time were examined through the variation of the quiescent gas pressures and secondary diaphragm thickness. Optimum operating conditions for helium test gas were also defined.

Shinn, J. L.↗
NASA NTRS1992

Application of program LAURA to perfect gas shock tube flows: A parametric study

The Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) was originally developed to solve steady-flow problems. The desire to validate the algorithm with shock tube experimental data motivated the development of a time-accurate version of the LAURA code. The current work presents a test of the Algorithm. Computational results are compared with the exact solution for a simple shock tube case. The parameters examined are Courant number, relaxation sweeps, grid spacing, and the inviscid relaxation factor. The results of the study indicate that LAURA is capable of producing accurate solutions when appropriate values are used for each parameter.

Mitterer, K. F.↗