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NASA NTRS1973

Time-split finite-volume method for three-dimensional blunt-body flow

An efficient numerical method for calculating plane, axisymmetric, and fully three-dimensional blunt-body flow is presented. It is a second-order-accurate, time-dependent finite-volume procedure that solves the Euler equations in integral conservation-law form. These equations are written with respect to a Cartesian coordinate system in which an embedded mesh adjusts in time to the motion of the bow shock that is automatically captured as part of the weak solution. With such an adjusting mesh, oscillations in flow properties near the shock are shown to be virtually eliminated. The scheme uses a time-splitting concept that accelerates the convergence appreciably. Comparisons are made between computed and experimental results.

Rizzi, A. W.↗

NASA NTRS1975

Pressure- and buoyancy-driven thermal convection in a rectangular enclosure

Results are presented for unsteady laminar thermal convection in compressible fluids at various reduced levels of gravity in a rectangular enclosure which is heated on one side and cooled on the opposite side. The results were obtained by solving numerically the equations of conservation for a viscous, compressible, heat-conducting, ideal gas in the presence of a gravitational body force. The formulation differs from the Boussinesq simplification in that the effects of variable density are completely retained. A conservative, explicit, time-dependent, finite-difference technique was used and good agreement was found for the limited cases where direct comparison with previous investigations was possible. The solutions show that the thermally induced motion is acoustic in nature at low levels of gravity and that the unsteady-state rate of heat transfer is thereby greatly enhanced relative to pure conduction. The nonlinear variable density profile skews the streamlines towards the cooler walls but is shown to have little effect on the steady-state isotherms.

Spradley, L. W.↗

NASA NTRS1976

Numerical solution of nonlinear partial differential equations of mixed type

A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

Jameson, A.↗

NASA NTRS1979

Acoustic behavior of a fibrous bulk material

A semiempirical model is presented describing the acoustic behavior of Kevlar 29, a bulk absorbing material. The model is based on an approximate solution to the one-dimensional equations representing conservation of fluctuating mass, momentum and energy. By treating the material as a momentum sink, theoretical expressions of the material complex propagation constants and characteristic impedance were derived in terms of a single constant. Evaluating the constant at a single frequency for a particular specimen, excellent agreement between prediction and measurement was achieved for a large range of sound frequencies and material porosities and thicknesses. Results show that Kevlar 29 absorbs sound efficiently even at low frequencies. This is explained in terms of a frequency dependent material phase speed.

Hersh, A. S.↗

NASA NTRS1979

Vector processor algorithms for transonic flow calculations

This paper discusses a number of algorithms for solving the transonic full-potential equation in conservative form on a vector computer, such as the CDC STAR-100 or the CRAY-1. Recent research with the 'artificial density' method for transonics has led to development of some new iteration schemes which take advantage of vector-computer architecture without suffering significant loss of convergence rate. Several of these more promising schemes are described and 2-D and 3-D results are shown comparing the computational rates on the STAR and CRAY vector computers, and the CYBER-175 serial computer. Schemes included are: (1) Checkerboard SOR, (2) Checkerboard Leapfrog, (3) odd-even vertical line SOR, and (4) odd-even horizontal line SOR.

South, J. C., Jr.↗

NASA NTRS1981

Computation of simple three-dimensional wing-vortex interaction in transonic flow

An implicit delta form finite-difference algorithm for Euler equations in conservation law form has been used in preliminary calculations of three-dimensional wing-vortex interactions. Both steady and unsteady transonic flow wing-vortex interactions are computed. The computations themselves are meant to guide upcoming wind tunnel experiments of the same flow field. Various modifications to the numerical method that are intended to improve computational efficiency are also described and tested in both two- and three-dimensions.

Srinivasan, G. R.↗

NASA NTRS1981

Computation of wing-vortex interaction in transonic flow using implicit finite difference algorithm

An implicit delta form finite difference algorithm for Euler equations in conservation law form was used in preliminary calculations of three dimensional wing vortex interaction. Both steady and unsteady transonic flow wing vortex interactions are computed. The computations themselves are meant to guide upcoming wind tunnel experiments of the same flow field. Various modifications to the numerical method that are intended to improve computational efficiency are also described and tested in both two and three dimensions. Combination of these methods can reduce the overall computational time by a factor of 4.

Srinivasan, G.↗

NASA NTRS1982

Development of a locally mass flux conservative computer code for calculating 3-D viscous flow in turbomachines

The VANS successive approximation numerical method was extended to the computation of three dimensional, viscous, transonic flows in turbomachines. A cross-sectional computer code, which conserves mass flux at each point of the cross-sectional surface of computation was developed. In the VANS numerical method, the cross-sectional computation follows a blade-to-blade calculation. Numerical calculations were made for an axial annular turbine cascade and a transonic, centrifugal impeller with splitter vanes. The subsonic turbine cascade computation was generated in blade-to-blade surface to evaluate the accuracy of the blade-to-blade mode of marching. Calculated blade pressures at the hub, mid, and tip radii of the cascade agreed with corresponding measurements. The transonic impeller computation was conducted to test the newly developed locally mass flux conservative cross-sectional computer code. Both blade-to-blade and cross sectional modes of calculation were implemented for this problem. A triplet point shock structure was computed in the inducer region of the impeller. In addition, time-averaged shroud static pressures generally agreed with measured shroud pressures. It is concluded that the blade-to-blade computation produces a useful engineering flow field in regions of subsonic relative flow; and cross-sectional computation, with a locally mass flux conservative continuity equation, is required to compute the shock waves in regions of supersonic relative flow.

Walitt, L.↗

NASA NTRS1982

Recent applications of the transonic wing analysis computer code, TWING

An evaluation of the transonic-wing-analysis computer code TWING is given. TWING utilizes a fully implicit approximate factorization iteration scheme to solve the full potential equation in conservative form. A numerical elliptic-solver grid-generation scheme is used to generate the required finite-difference mesh. Several wing configurations were analyzed, and the limits of applicability of this code was evaluated. Comparisons of computed results were made with available experimental data. Results indicate that the code is robust, accurate (when significant viscous effects are not present), and efficient. TWING generally produces solutions an order of magnitude faster than other conservative full potential codes using successive-line overrelaxation. The present method is applicable to a wide range of isolated wing configurations including high-aspect-ratio transport wings and low-aspect-ratio, high-sweep, fighter configurations.

Subramanian, N. R.↗

NASA NTRS1982

Transonic perturbation analysis of wing-fuselage-nacelle-pylon configurations with powered jet exhausts

A transonic small perturbation method has been developed for the analysis of general wing-fuselage-nacelle-pylon configurations with powered jet exhausts. Finite difference successive line relaxation algorithm is used to solve the small disturbance potential equation in conservative form. The nacelle tangency condition and the jet exhaust plume contact conditions are fulfilled in a quasi-cylindrical fashion on a surface fitting the Cartesian grid. The pylon tangency condition is treated in a quasi-planar manner as for the wing. Viscous displacement effects on the wing are modeled by suitable shape changes including the placement of a viscous ramp at the base of the shock. Computed results of a transport configuration show satisfactory correlation with test data.

Wai, J. C.↗

NASA NTRS1981

On the formation of protostellar disks

An analysis is presented of the hydrodynamic aspects of the growth of protostellar disks from the accretion of a rotating gas cloud. Streamline equations for the flow onto the disk are derived, including the special case where the disk is very thin. For the radial structure of the disk, detailed equations of conservation of mass, momentum, angular momentum, and energy are given. Exact solutions are found for the case of no internal viscosity. For the more general case where there is viscous stress, hypotheses are formulated with the objective of discovering the main qualitative characteristics of a turbulent system and to estimate the magnitude of the turbulent stress. Solutions are also found for boundary conditions, and the large and small viscosity limits. The relation of energy balance to disk thermal structure is detailed. Finally, trends in the collapse of the dust cloud are discussed in the light of the solutions given.

Cassen, P.↗

NASA NTRS1981

Treatment of conical and nonconical supersonic flows by an implicit marching scheme applied to the full potential equation

An aerodynamic prediction technique based on the full potential equation in conservation form is developed for the treatment of supersonic flows. This technique bridges the gap between simplistic linear theory methods and complex Euler solvers. A novel local density linearization concept and a second order accurate retarded density scheme, both producing the correct artificial viscosity, are introduced in developing an implicit marching scheme for solving the scalar potential. Results for conical flows over delta wings and a wing-body combination and for non-conical flows over bodies of revolution at angles of attack are compared with Euler and nonconservative full potential calculations and experimental data. The present formulation requires an order of magnitude less computer time and significantly less computer memory over Euler codes and exhibits a considerable improvement in computational efficiency and generality over an existing nonconservative full potential code.

Shankar, V.↗

NASA NTRS1982

The photochemical heating of the cometary atmosphere

A self-consistent solution of the thermodynamic structure of an H2O-dominated multispecies cometary atmosphere at 1 AU is obtained by solving the simultaneous set of differential equations representing conservation of number density, momentum, energy, and the flux of solar UV radiation in the three streams responsible for the major photolytic processes. The relative efficiency of the expansion and infrared cooling by H2O over the photolytic heating by the UV radiation in the inner coma brings about a rapid decrease in the temperature there, reaching a minimum of only about 5.4 K at a nuclear distance of approximately 54 km. Thereafter, the temperature is found to increase to about 810 K at a nuclear distance of 25,000 km, owing to higher efficiency of the photolytic heating over the cooling process. The expansion in the inner coma is seen to be highly supersonic, attaining a maximum Mach number of about 15 at the distance of temperature minimum. After that, the Mach number steadily decreases, reaching a value of about 2.3 at a nuclear distance of 25,000 km.

Marconi, M. L.↗

NASA NTRS1982

A full potential inverse method based on a density linearization scheme for wing design

A mixed analysis inverse procedure based on the full potential equation in conservation form was developed to recontour a given base wing to produce density linearization scheme in applying the pressure boundary condition in terms of the velocity potential. The FL030 finite volume analysis code was modified to include the inverse option. The new surface shape information, associated with the modified pressure boundary condition, is calculated at a constant span station based on a mass flux integration. The inverse method is shown to recover the original shape when the analysis pressure is not altered. Inverse calculations for weakening of a strong shock system and for a laminar flow control (LFC) pressure distribution are presented. Two methods for a trailing edge closure model are proposed for further study.

Shankar, V.↗

NASA NTRS1982

The photochemistry and dynamics of a dusty cometary atmosphere

The solving of a simultaneous set of differential equations representing conservation of number density, momentum, and energy together with solar radiation transfer in the streams which result in photolytic processes and the heating of the nucleus yields a self-consistent solution of the dynamical and thermal structure of an H2O-dominated two-phase dusty gas cometary atmosphere. Two models are considered for the transfer of solar radiation through the circumnuclear dust halo. The first considers only the direct extinction by the dust, and in the second the diffuse radiation field due to multiple scattering by the dust halo, which compensates for radiation removed by direct absorption when the optical depth is near unity, is approximated by neglecting the attenuation of radiation given off by the dust. It is shown that while dust attenuation has a strong effect on the H2O production rate, it also increases the electron density in the inner coma over the unattenuated case.

Marconi, M. L.↗

NASA NTRS1983

A new consistent spatial differencing scheme for the transonic full-potential equation

A new spatial differencing scheme for the transonic full-potential equation in conservative form has been developed. This scheme guarantees zero truncation error on any curvilinear mesh for freestream flows in either two- or three-space dimensions. Solutions obtained with this new differencing scheme, away from freestream regions, exhibit greatly improved accuracy, especially for nonsmooth or singular meshes.

Flores, J.↗

NASA NTRS1983

Transonic flow simulation of prop-fan configurations

This paper presents the results of a study that used a three-dimensional transonic analysis method to analyze flow around a wing-mounted prop-fan configuration. The transonic analysis method employs a cell-oriented finite volume approach to solve the full potential equation in conservative form over a numerically generated surface-fitted grid. The propeller slipstream effects are simulated using a linearized transpiration boundary condition. The results of analyses of flow over clean wing/body, wing/body/nacelle, and wing/body nacelle with slipstream are compared to test data.

Samant, S. S.↗

NASA NTRS1982

A multi-fluid model of an H2O-dominated dusty cometary atmosphere

The solution of the simultaneous set of differential equations representing conservation of number density, momentum, and energy, together with solar radiation transfer in streams that are responsible for major photolytic processes and nucleus heating, yields a self-consistent multifluid solution for the thermal and dynamical structure of an H2O-dominated, two-phase dusty gas cometary atmosphere, whose validity is restricted to the collision-dominated region where ions and neutrals are assumed to achieve a common temperature and velocity. The model is transonic, due to the dust in the inner coma, and involves the subsonic expansion of the ions and neutrals from the nucleus until, in the outermost part of the collision-dominated coma, temperatures of 300-400 K are reached due to UV pyrolytic heating.

Marconi, M. L.↗