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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Computation of the inviscid supersonic flow over an external axial corner

A second-order finite-difference procedure is used to evaluate the inviscid supersonic flowfield surrounding an external axial corner composed of swept planar compression surfaces and representing the inlets on existing high-speed aircraft. The governing partial differential equations in conservation-law form are hyperbolic with respect to the axial coordinate and are solved iteratively by means of MacCormack's algorithm. The procedure treats both the peripheral shock wave and vortical singularities as discontinuities. Numerical results are presented for two parametric studies regarding the effects on the flowfield of varying the free-stream Mach number and the leading edge sweep of the horizontal wedge. Results of parametric Mach number study agree with the Mach number independence principle in that as the Mach number increases, such characteristics as shock shape, cross-flow sonic line location, and vortical singularity position approach an asymptote.

Kutler, P.↗
NASA NTRS1976

Diffraction of a shock wave by a compression corner. I - Regular reflection

The unsteady, two-dimensional flowfield resulting from the interaction of a moving planar shock wave with a compression corner is determined using a second-order, discontinuity-fitting, finite-difference approach. The time-dependent Euler equations are transformed to normalize the distance between the body and peripheral shock and to include the existing self-similar property of the flow. The resulting set of partial differential equations in conservation-law form is then solved in a time-dependent fashion using MacCormack's scheme. The vortical singularity, which lies on the body surface, and the single reflected shock are both treated as discontinuities in the numerical procedure. The results of the numerical simulation compare quite favorably with existing experimental interferograms and yield better flowfield resolution than previous first-order, shock-capturing, numerical solutions.

Kutler, P.↗
NASA NTRS1976

A numerical study of viscous flow around an airfoil

An integrodifferential method, previously formulated in terms of velocity and vorticity vectors, is reformulated in terms of stream function and vorticity for two-dimensional incompressible viscous flows. The reformulated integrodifferential method is shown to retain the distinguishing feature of the previous formulation in permitting the confinement of the solution field to the viscous region of the flow and consequently offers great computational advantages. The application of this procedure in a study of an incompressible flow around an impulsively started 9% thick symmetric Joukowski airfoil at an angle of attack of 15 deg and a Reynolds number of 1000 is discussed. Numerical results are presented and compared with available finite-difference results.

Wu, J. C.↗
NASA NTRS1976

Numerical solution of periodic transonic flow through a fan stage

A numerical method of solution of the inviscid, compressible, two-dimensional unsteady flow on a blade-to-blade stream surface through a stage (rotor and stator), or a single blade row, of an axial flow compressor or fan is described. A cyclic procedure has been developed for representation of adjacent blade-to-blade passages, which asymptotically achieves the correct phase between all passages of a stage. A shock-capturing finite-difference method is employed in the interior of the passage, and a method-of-characteristics technique is used at the boundaries. The blade slipstreams form two of the passage boundaries, and are treated as moving contact surfaces capable of supporting jumps in entropy and tangential velocity. The Kutta condition is imposed by requiring the slipstreams to originate at the trailing edges, which are assumed to be sharp. Results are presented for several transonic fan rotors, and compared with available experimental data consisting of holographic observations of shock structure and pressure contour maps. A subcritical stator solution is also compared with results from a relaxation method. Finally, a periodic solution for a stage consisting of 44 rotor blades and 46 stator blades is discussed.

Erdos, J. I.↗
NASA NTRS1976

Two inviscid computational simulations of separated flow about airfoils

Two inviscid computational simulations of separated flow about airfoils are described. The basic computational method is the line relaxation finite-difference method. Viscous separation is approximated with inviscid free-streamline separation. The point of separation is specified, and the pressure in the separation region is calculated. In the first simulation, the empiricism of constant pressure in the separation region is employed. This empiricism is easier to implement with the present method than with singularity methods. In the second simulation, acoustic theory is used to determine the pressure in the separation region. The results of both simulations are compared with experiment.

Barnwell, R. W.↗
NASA NTRS1976

Investigation of slot cooling at high subsonic speeds

The paper discusses the results of an experimental and numerical investigation of tangential slot injection film cooling with zero pressure gradients in subsonic boundary layers at freestream Mach numbers of 0.4, 0.6, and 0.8. The results are compared with the predictions obtained from a finite-difference boundary-layer program developed by NASA for slot injection into turbulent supersonic boundary layers. The two sets of results are found to compare favorably. The numerical results point to the existence of a unique relation between isothermal effectiveness and adiabatic effectiveness, thereby confirming the existence of similarity conditions for temperature and velocity profiles.

Ferri, A.↗
NASA NTRS1976

A note on the leap-frog scheme in two and three dimensions

The paper considers the leap-frog finite-difference method (Kreiss and Oliger, 1973) for systems of partial differential equations of the form du/dt = dF/dx + dG/dy + dH/dz, where d denotes partial derivative, u is a q-component vector and a function of x, y, z, and t, and the vectors F, G, and H are functions of u only. The original leap-frog algorithm is shown to admit a modification that improves on the stability conditions for two and three dimensions by factors of 2 and 2.8, respectively, thereby permitting larger time steps. The scheme for three dimensions is considered optimal in the sense that it combines simple averaging and large time steps.

Abarbanel, S.↗
NASA NTRS1976

High-latitude truncation errors of box-type primitive equation models

The 'box-type' finite-difference method includes a weighted average of the pressure gradient with weights proportional to the surface of the grid walls. It is shown that this averaging introduces first-order truncation errors near the poles. An example is shown in which the relative error is of zero order and the scheme produces large distortions in the solution at high latitudes.

Kalnay-Rivas, E.↗
NASA NTRS1976

A two-dimensional finite difference solution for the transient thermal behavior of tubular solar collector

A numerical procedure was established using the finite-difference technique in the determination of the time-varying temperature distribution of a tubular solar collector under changing solar radiancy and ambient temperature. Three types of spatial discretization processes were considered and compared for their accuracy of computations and for selection of the shortest computer time and cost. The stability criteria of this technique was analyzed in detail to give the critical time increment to ensure stable computations. The results of the numerical analysis were in good agreement with the analytical solution previously reported. The numerical method proved to be a powerful tool in the investigation of the collector sensitivity to two different flow patterns and several flow control mechanisms.

Lansing, F. L.↗
NASA NTRS1976

A brief description of the Jameson-Caughey NYU transonic swept-wing computer program: FLO 22

A computer program for analyzing inviscid, isentropic, transonic flow past 3-D swept configurations is presented. Some basic aspects of the program are: (1) the free-stream Mach number is restricted only by the isentropic assumption; (2) weak shock waves are automatically located wherever they occur in the flow; (3) the finite-difference form of the full equation for the velocity potential is solved by the method of relaxation, after the flow exterior to the airfoil is mapped to the upper half plane; (4) the mapping procedure allows exact satisfaction of the boundary conditions and use of supersonic free stream velocities; (5) the finite difference operator is locally rotated in supersonic flow regions so as to properly account for the domain of dependence; and (6) the relaxation algorithm was stabilized using criteria from a time-like analogy.

Jameson, A.↗
NASA NTRS1976

The nonlinear transient response of thin, rectangular elastic plates

The results of experiments and theoretical analysis of the nonlinear, transient response of thin, rectangular, elastic, simply supported plates are presented. In the experiments, a plane wave tube with a special pulse generator at one end and a thin glass plate mounted at the other end was used to subject the glass plate to pressure pulses of different magnitudes. Whole-field measurements of the response of the plate were obtained by the reflected moire grid technique. The largest ratio of center deflection to thickness of the plate during the experiments was 5.6. The theoretical response of the glass plate to the pressure pulses was computed by solving the von Karman equations governing large deflections in elastic plates by two methods - (1) the finite-difference method, and (2) Galerkin's method. Good agreement was found between theoretically predicted and experimentally measured response.

Rajagopal, G.↗
NASA NTRS1976

Improved interactive calculation procedure for supersonic flows

An interactive numerical procedure has been developed for supersonic viscous flows (either two-dimensional or axisymmetric configurations). The flow field is divided into two regions: (1) an inner region which is highly viscous and mostly subsonic, and (2) an outer region where the flow is supersonic and in which viscous effects are small, but not negligible. This paper presents a detailed description of: I. Outer Region - numerical solution obtained by applying the method of characteristics to a system of equations which includes viscous and conduction transport terms only normal to the streamlines; II. Inner Region - treated by a system of equations of the boundary-layer type that includes higher order effects, such as longitudinal and transverse curvature and normal pressure gradients (equations are coupled and solved simultaneously in physical coordinates, using an implicit finite-difference scheme); III. Interactive Procedure - in the interaction mode, the two regions are coupled iteratively along a matching line, where the Mach number is of the order of 1.2.

Tassa, Y.↗
NASA NTRS1976

Numerical solutions of the triple-deck equations for laminar trailing-edge stall

The problem of determining the effect of laminar boundary layers on the lift of thin wings in subsonic flow at high Reynolds numbers is considered. The boundary value problem is formulated in the framework of the triple-deck theory of Brown and Stewartson. The resulting fourth-order boundary value was solved by an iterative finite-difference technique. An inverse iteration procedure provides proper treatment of the trailing-edge singularity, and asymptotic far-field expansions and coordinate stretchings are used to deal with the problem of the slow algebraic decay of the solution.

Chow, R.↗
NASA NTRS1976

Impact ejecta on the moon

The response of a lunar-sized object to the impact of meteoroids no more than about 100 km in radius is studied by means of a numerical model. The partitioning of impact energy into the kinetic and internal energy of the ejecta is obtained by using the conservation of mass, momentum, and energy conservation equations in finite-difference form within an Eulerian framework with approximate equations of state. The calculations are performed for a 15 km/sec impact of an iron object 5 cm in radius on a gabbroic anorthosite surface. Ejecta ballistic analysis is then performed. Most of the material lost escaping the moon is lunar crust material. Only 0.2% of the meteoroid escapes, all in the vapor phase.

Okeefe, J. D.↗
NASA NTRS1976

Numerical solution of the steady-state Navier-Stokes equations for hypersonic flow about blunt axisymmetric bodies

The steady-state Navier-Stokes equations are solved for hypersonic flow about blunt axisymmetric bodies. The equations of motion are solved by successive approximations using an implicit finite-difference scheme. The results are compared with viscous shock-layer theory, experimental data, and time-dependent solutions of the Navier-Stokes equations. It is demonstrated that viscous shock-layer theory is sufficiently accurate for the range of flight conditions normally encountered by entry vehicles.

Anderson, E. C.↗
NASA NTRS1947

Determination of elastic stresses in gas-turbine disks

A method is presented for the calculation of elastic stresses in symmetrical disks typical of those of a high-temperature gas turbine. The method is essentially a finite-difference solution of the equilibrium and compatibility equations for elastic stresses in a symmetrical disk. Account can be taken of point-to-point variations in disk thickness, in temperature, in elastic modulus, in coefficient of thermal expansion, in material density, and in Poisson's ratio. No numerical integration or trial-and-error procedures are involved and the computations can be performed in rapid and routine fashion by nontechnical computers with little engineering supervision. Checks on problems for which exact mathematical solutions are known indicate that the method yields results of high accuracy. Illustrative examples are presented to show the manner of treating solid disks, disks with central holes, and disks constructed either of a single material or two or more welded materials. The effect of shrink fitting is taken into account by a very simple device.

Manson, S S↗
NASA NTRS1950

Direct method of design and stress analysis of rotating disks with temperature gradient

A method is presented for the determination of the contour of disks, typified by those of aircraft gas turbines, to incorporate arbitrary elastic-stress distributions resulting from either centrifugal or combined centrifugal and thermal effects. The specified stress may be radial, tangential, or any combination of the two. Use is made of the finite-difference approach in solving the stress equations, the amount of computation necessary in the evolution of a design being greatly reduced by the judicious selection of point stations by the aid of a design chart. Use of the charts and of a preselected schedule of point stations is also applied to the direct problem of finding the elastic and plastic stress distribution in disks of a given design, thereby effecting a great reduction in the amount of calculation. Illustrative examples are presented to show computational procedures in the determination of a new design and in analyzing an existing design for elastic stress and for stresses resulting from plastic flow.

Manson, S S↗
NASA NTRS1961

Cross-Sectional Deformations of Monocoque Beams and Their Effects on the Natural Vibration Frequencies

The variational principle, differential equations, and boundary conditions governing the cross-sectional distortions due to inertia loading of a two-dimensional model of a thin monocoque wing are shown. A theoretical analysis of this simplified model is made in order to determine the nature of the coupling between the cross-sectional modes and the spanwise deformation modes. General solutions are obtained in finite-difference form for arbitrary cross sections and an exact solution is presented for a parabolic-arc cross section of constant cover thickness. The application of these results in evaluating the coupled frequencies of the actual structure is discussed. Frequencies evaluated for a parabolic-arc monocoque beam show good agreement with experimental values.

Thomson, Robert G.↗